Variation of constant formula for first order fuzzy differential equations111111.pdf

《Variation of constant formula for first order fuzzy differential equations111111.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、FuzzySetsandSystems177(2011)2033www.elsevier.com/locate/fssVariationofconstantformulaforfirstorderfuzzydifferentialequationsA.Khastana,b,∗,J.J.Nietoa,RosanaRodríguez-LópezaaDepartamentodeAnálisisMatemático,FacultaddeMatemáticas,UniversidaddeSantiagodeCompos

2、tela15782,SantiagodeCompostela,SpainbDepartmentofMathematics,InstituteforAdvancedStudiesinBasicSciences,Zanjan45137-66731,IranReceived16December2009;receivedinrevisedform17February2011;accepted26February2011Availableonline5March2011AbstractInthispaper,west

3、udyfirstorderlinearfuzzydifferentialequationsbyusingthegeneralizeddifferentiabilityconceptandwepresentthegeneralformoftheirsolutions.Wealsocorrectandcompletesomepreviousresults.Finally,someexamplesaregiventoillustrateourresults.©2011ElsevierB.V.Allrightsres

4、erved.Keywords:Firstorderfuzzydifferentialequations;Generalizeddifferentiability;Fuzzylineardifferentialequations1.IntroductionFirstorderlinearfuzzydifferentialequationsareoneofthesimplestfuzzydifferentialequationswhichmayappearinmanyapplications.TheH-deri

5、vativeofafuzzy-number-valuedfunctionwasintroducedin[19].Underthissetting,theexistenceanduniquenessofthesolutionofafuzzydifferentialequationarestudied(forexample,in[5,12]).Thisapproachhasthedisadvantagethatitleadstosolutionswhichhaveanincreasinglengthofthei

6、rsupport[8].Fuzzydifferentialequationshavebeenstudiedunderotherapproaches(see[6,11,15,18]).Firstorderlinearfuzzydifferentialequationsorsystemsarestudiedunderdifferentinterpretationsinseveralpapers(see[5,8,13,17]).Thesolutionsprovidedinthesepapersusuallypre

7、sentsomesimilaritytothevariationofconstantsformulabuttheseresultshavethedisadvantagementionedabove[9].Recently,avariationofconstantsformulaforafuzzyfractionaldifferentialequationispresentedin[1].In[4],firstorderlinearfuzzydifferentialequationsundergeneraliz

8、eddifferentiabilityconceptareconsideredandsolutionsofthisprobleminsomeespecialcaseswerepresented.Seealso[20]forsomeresultsonintervaldifferentialequations.In[16]alinearfuzzynucleardecayequationundergeneralized